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I'm studying 12th. In my book they mentioned that $\ce{[Co(en)3]^3+}$ exhibits optical isomerism.

But in that same book, there is a question

Which of this doesn't exhibit isomerism?

and the answer is $\ce{[Fe(en)3]^3+}.$ Since both complexes have the same structure, then why they are saying $\ce{[Fe(en)3]^3+}$ doesn't show isomerism?

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    $\begingroup$ It would be nice if you could add the citation for your book, including author(s), title, edition, publisher, year, page number(s) and IDs (e.g. ISBN). On Chemistry.SE, ACS citation style is preferred. $\endgroup$ – andselisk Mar 20 at 12:17
  • $\begingroup$ It is my textbook!! $\endgroup$ – Vijay Mar 20 at 12:41
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    $\begingroup$ Good news: you can cite your textbooks as well. $\endgroup$ – andselisk Mar 20 at 12:42
  • $\begingroup$ Okay. They gave these options.. $\endgroup$ – Vijay Mar 20 at 12:52
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    $\begingroup$ That's not at all what I'm asking. "To cite" means to provide extensive bibliographic information about your source. $\endgroup$ – andselisk Mar 20 at 12:59
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I think the answer given in your textbook is either incorrect or a misprint. I let you find out the correct answer from given choices.

However, I'd like like to claim that the given answer is wrong because of following facts:

  • Tris(ethylenediamine) complexes of transition metals have been studied for more than 100 years and $\ce{M(en)3^3+}$ complexes are been considered chiral (e.g., Ref.1 for studies on $\ce{Co(en)3^3+}$).
  • The enanti­omeric nature of these complexes has been verified by X-ray crystallography (e.g., Ref.2 for studies on $\ce{Co(en)3^3+}$).
  • The crystal structures of the first-row transition-metal series of tris­­(ethyl­enedi­amine) di­acetate complexes have been recently studied (Ref.3) to show their chiral nature, and following common structure is given for the complexes with $\ce{M^2+}$ central metal:

tris­­(ethyl­enedi­amine) di­acetate complexes

The abstract states that:

The crystal structures of the first-row transition-metal series of tris­(ethyl­enedi­amine-$\kappa^2$N,N′)metal(II) di­acetate, $\ce{[M(C2H8N2)3](CH3CO2)2}$, with $\ce{M = Mn, Fe, Co, Ni, Cu,}$ and $\ce{Zn}$, are reported. The complexes are all isostructural, crystallizing in a centrosymmetric triclinic cell and possessing an asymmetric unit composed of one $\ce{[M(en)3]^2+}$ cation and two symmetrically independent acetate anions. In the unit cell, the two complex cations are inversion-generated enanti­omers, possessing the energetically favoured Δ(λλλ) and Λ(δδδ) configurations. The complex cations and acetate anions combine through a series of $\ce{N—H⋯O}$ hydrogen bonds to generate a three-dimensional network in the crystals. The other notable feature of the series is a significant Jahn–Teller distortion for the $\mathrm{d^9}$ $\ce{Cu^2+}$ complex.

It is a fact that structures of these same first-row transition-metal series with 3+ oxidation state would give the same octahedral shapes, the cation of which are chiral (e.g., Ref.1 and Ref.2). Examples of few are given below:

Metal 3+ Complexes

Overall, it is true that the $\ce{[Fe(en)3]^3+}$ cation is chiral.

References:

  1. A. Werner, "Zur Kenntnis des asymmetrischen Kobaltatoms. V," Berichte der deutschen chemischen Gesellschaft 1912, 45(1), 121-130 (https://doi.org/10.1002/cber.19120450116).
  2. Y. Saito, K. Nakatsu, M. Shiro, H. Kuroya, "The first-row transition-metal series of tris­­(ethyl­enedi­amine) di­acetate Determination of the absolute configuration of optically active complex ion, $\ce{[Co(en)3]^3+}$, by means of X-rays," Acta Crystallographica 1955, 8, 729-730 (https://doi.org/10.1107/S0365110X55002211).
  3. Duyen N. K. Pham, Mrittika Roy, James A. Golen, David R. Manke, "The first-row transition-metal series of tris­­(ethyl­enedi­amine) di­acetate complexes M(en)32 (M is Mn, Fe, Co, Ni, Cu, and Zn)," Acta Crystallographica Section C 2017, 73(6), 442-446 (https://doi.org/10.1107/S2053229617006738).
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    $\begingroup$ this answer misses an important point. The individual ions in the structure are chiral but the overall crystal is not. $\endgroup$ – matt_black Mar 21 at 16:32
  • $\begingroup$ @matt_black: The major point of the question is chirality of the complex ion, not the crystal structure. Crystallography is one way to show the absolute stereochemistry. The crystal coordination shows that. Should have read the article. $\endgroup$ – Mathew Mahindaratne Mar 21 at 20:20
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    $\begingroup$ Take my comment as a suggestion for ow to make your answer clearer. Had you added a simple sentence explaining the point I made, the answer would be totally fine. But that point is buried in useful but unnecessary detail. $\endgroup$ – matt_black Mar 21 at 21:47
  • $\begingroup$ @matt_black: Finally, I got your point. I was only try to point out that OP's textbook statement is incorrect. I apologize for my ignorance. The answer has been corrected since. $\endgroup$ – Mathew Mahindaratne Mar 21 at 22:37

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